The Source of Primeness of Rings

Yıl 2022, Sayı: 41, 100 - 104, 31.12.2022

Didem Yeşil , Didem Karalarlıoğlu Camcı

https://doi.org/10.53570/jnt.1189651

Cited By: 1

Öz

In this study, we define a new concept, i.e., source of primeness of a ring $R$, as $P_{R} := \bigcap_{a\in R} S_{R}^{a}$ such that $S_{R}^{a}:=\{b\in R \mid aRb=(0)\}$. We then examine some basic properties of $P_{R}$ related to the ring’s idempotent elements, nilpotent elements, zero divisor elements, and identity elements. Finally, we discuss the need for further research.

Anahtar Kelimeler

Prime ring, semiprime ring, source of primeness, source of semiprimeness

Kaynakça

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